On Generalizations of Dickson k-Fibonacci Polynomials

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ÖZKAN E., Akkus H.

WSEAS Transactions on Mathematics, cilt.23, ss.856-862, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23
  • Basım Tarihi: 2024
  • Doi Numarası: 10.37394/23206.2024.23.88
  • Dergi Adı: WSEAS Transactions on Mathematics
  • Derginin Tarandığı İndeksler: Scopus, INSPEC, zbMATH
  • Sayfa Sayıları: ss.856-862
  • Anahtar Kelimeler: Binet formula, Cassini Identity, Dickson polynomials, Fibonacci sequence, Generating function, Key-Words: - k-Fibonacci polynomials
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Marmara Üniversitesi Adresli: Hayır

Özet

- In this study, we define a Dickson k-Fibonacci polynomial inspired by Dickson polynomials and give some terms of these polynomials. Then we present the relations between the terms of Dickson k-Fibonacci polynomials. We find Binet formulas and generating functions for these polynomials. In addition, we give some important identities like Catalan identity, Melham’s identity, and Gelin-Cesaro’s identity. Moreover, Catalan transformation is applied to these polynomials, and their terms are found. Finally, the Hankel transform is applied to the Catalan transform of these polynomials, and the results obtained are associated with known Fibonacci numbers.